Nodes with cases with TikZ

I need to make something that should look like this (sorry for such low quality of picture)

So I type this but it's doesn't work correctly:

\begin{tikzpicture}

\node (A) at (0,0) {$\vec{\bf r} = \vec{\bf R}(\vec{\bf r},\bf t)$};

\node (B) at (0, 20)
{$$\begin{cases} { X_1 = X_1(X_1,X_2,X_3,t) }; \dots { x_3 = x_3(X_1,X_2,X_3,t) }; \end{cases};$$}

\draw[->] (A) -| node[near start,below]  (B);

\end{tikzpicture}


Here are some errors (which are related to this code part) from .log:

line 0: Argument of \tikz@scan@no@calculator has an extra }
line 0: Package tikz Error: Giving up on this path. Did you forget a semicolon?
line 277: Bad math environment delimiter. {$line 277: Missing$ inserted {$X_ line 277: Missing \cr inserted {$ X_1 = X_1(X_1,X_2,X_3,t) $} line 0: Misplaced \crcr line 0: Missing \endgroup inserted line 283: Missing$ inserted \]
line 283: Missing } inserted \]
line 284: Package tikz Error: Giving up on this path. Did you forget a semicolon? $} line 285: Missing$ inserted I've inserted a begin-math/end-math symbol since I think

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That example gives all kinds of problems if you do not load the correct packages, would you mind updating you question with proper loading of packages for a full MWE? Welcome to TeX SE! :) –  zeroth Sep 28 '12 at 17:42
In this example, you are trying to start a displaymath environment within , you could try removing the $ and $ and see if it helps. –  T. Verron Sep 29 '12 at 8:33

One possibility using a matrix of math nodes:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,positioning}

\begin{document}

\begin{tikzpicture}[every left delimiter/.style={xshift=1ex}]
\node (r) {$\vec{r}=\vec{r}(\vec{R},t)$};
\matrix[matrix of math nodes,left delimiter=\lbrace,below = 10pt of r] (mat)
{
x_1 = F(x) \\
\cdots \\
x_1 = F(x) \\
};
\draw[->,shorten >= 6pt] (r.west) -- +(-15pt,0) |- (mat);
\end{tikzpicture}

\end{document}


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Oh thank you so much! –  Danil Gholtsman Sep 28 '12 at 17:47